Simulation · Electromagnetism

RC Circuit Simulation

Reading time: 6 minConfidence: HighLast verified: July 2026

This simulation plots the exponential charging and discharging curves of a resistor-capacitor (RC) circuit in real time, letting you adjust resistance, capacitance, and supply voltage and see how the time constant τ = RC controls the speed of charge and discharge.

Interactive simulation

Resistance R (kΩ)10 Capacitance C (µF)10 Supply Voltage (V)9

Time constant τ: — ms

Capacitor voltage: — V

Circuit current: — mA

Elapsed time: — ms

The physics behind this simulation

When a capacitor charges through a resistor from a supply voltage V₀, its voltage follows an exponential approach to the supply voltage:

V_C(t) = V₀(1 − e⁻ᵀ¹ₕᵀ⁾⁾ᵏₕ⁾⁾ₕₕ), τ = RC

When discharging (supply disconnected, capacitor discharging through the resistor), the voltage instead decays exponentially from its starting value toward zero: V_C(t) = V₀e⁻ᵀ¹ₕᵀ⁾⁾ᵏₕ⁾⁾ₕₕ. In both cases, τ = RC (the time constant) is the time for the voltage to close roughly 63% of the remaining gap to its final value — a single, convenient number capturing how "fast" a given RC circuit responds.

Common mistakeThe capacitor never mathematically reaches exactly full charge (or exactly zero on discharge) in finite time — the exponential only approaches its limit asymptotically. In practice, after about 5τ, the capacitor is charged (or discharged) to over 99% of its final value, which is why "5 time constants" is the usual practical rule of thumb for "fully charged" in circuit design.

Sources

Halliday, D., Resnick, R., Walker, J. (2013). Fundamentals of Physics, 10th ed. Wiley, Ch. 27.

Last verified: July 2026 · Source: Halliday, Resnick & Walker (2013) · Confidence: high

Interactive simulation

The physics behind this simulation

Sources

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